Parabolic tooth trace gear mechanism with combined tooth profile of end face circular arc and parabola

The present disclosure relates to the technical field of transmission gears, in particular to a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola.

Gears are widely used in industrial equipment such as a robot joint reducer, an automobile gearbox, a wind power gearbox, a headstock of a machine tool, etc., which transmits motion and power and is regarded as the “heart” of machines. At present, it is difficult for the transmission of a spur gear, a helical gear, a circular arc gear of a conventional involute and other parallel-axis cylindrical gears to overcome the problems of transmission failure such as frictional wear, gluing and plastic deformation, thermal deformation, vibration and noise resulted from relative sliding of tooth surfaces. At the same time, a gear lubrication system increases the weight and cost of the whole machine. In extreme environments such as high temperature, low temperature, high pressure, vacuum and strong radiation, the lubricant may fail, and its discharge also results in irreversible pollution to the environment. With the rapid development of the intelligent manufacturing industry, conventional gear products cannot meet the precision transmission requirements of high-end equipment such as an automobile automatic transmission, a robot reducer, a wind power gearbox and a high-speed rail transit, and high-performance gear products rely heavily on imports. The high-performance gear design and manufacturing technology has become a key factor restricting the development of the high-end equipment manufacturing field. How to avoid relative sliding of the tooth surface and improve the gear transmission performance is one of the key problems to be solved urgently in this field.

In order to solve the problems existing in the above-mentioned parallel shaft gear transmission, researchers at home and abroad have successively invented single-arc gears, double-arc gears and circular arc tooth trace cylindrical gears. For example, Chinese patent document with application No. 202110318591.7 discloses “DOUBLE-ARC REDUCTION TRANSMISSION DEVICE WITH LESS TOOTH DIFFERENCE AND METHOD OF FORMING DOUBLE-ARC TEETH”, and Chinese patent document with application No. 202123012746.9 discloses “CYLINDRICAL GEAR PAIR STRUCTURE WITH VARIABLE HYPERBOLIC circular arc TOOTH TRACE”. However, the tooth profiles of the small wheel and the big wheel of double-arc gears are cut by a generating cutting method based on the same hob. In order to ensure the correct meshing of large gears and small gears, the pressure angles of two meshing points of the tooth profile of the hob are set as equal values. Therefore, the limitation of the existing double-arc gear mechanism is that its structure is not the optimal bearing design structure because the pressure angles of two meshing points of the tooth profile are defined to be equal. When the loaded mechanical equipment bears heavy load transmission, the gear teeth may be broken, which may lead to accidents. The tooth surface design of the above-mentioned hyperbolic circular arc tooth trace cylindrical gear pair is limited by machining cutter head parameters. The tooth tips at both ends will become sharp. The effective contact area of the tooth surfaces is only concentrated in the limited area of the center of the tooth width. Therefore, when applied to heavy load transmission, there is a risk of breaking gear teeth. At the same time, the relative sliding of the tooth surfaces leads to serious frictional wear.

In view of this, in order to solve the problems in the prior art that the effective contact area of the tooth surfaces in the gear mechanism is only concentrated in the limited area of the center of the tooth width, there is a risk of breaking gear teeth, the relative sliding of the tooth surfaces is large, and frictional wear is serious, the embodiment of the present disclosure provides a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola.

Embodiments of the present disclosure provide a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola, including a gear pair consisting of a small wheel and a big wheel with parallel axes, and pure rolling meshing transmission is performed between the small wheel and the big wheel, wherein: end face tooth profile curves of the small wheel and the big wheel consist of an end face working tooth profile curve and a tooth root transition curve, and the end face tooth profile curves of the small wheel and the big wheel are symmetrical on the left and right sides; end face working tooth profiles of the small wheel and the big wheel are the combined tooth profiles of the end face circular arc and the parabola; tooth surfaces of the small wheel and the big wheel have parabolic tooth trace structures; at least one pair of gear teeth meshing points of the small wheel and the big wheel are located at a node to implement pure rolling meshing contact, and relatively rotating meshing points of the small wheel and the big wheel form meshing lines, and two contact lines are formed on the tooth surfaces of the small wheel and the big wheel, respectively.

Further, tooth surface structures of the small wheel and the big wheel are formed by the motion of the end face tooth profile curves of the small wheel and the big wheel along a tooth surface contact line with a contact point, and the contact line is an axisymmetric parabola after being unfolded along a pitch cylindrical surface of the small wheel and the big wheel.

Further, left working tooth profile curves of the end face of the small wheel and the big wheel are formed by smoothly connecting two plane curves (a circular arc and a parabola) at an inter-tooth control point P, an inter-tooth control point Gof a right tooth profile coincides with a node Pwhen the small wheel and the big wheel are installed, and the control point Gis obtained by the axial symmetry of the inter-tooth control point Pof a left working tooth profile curve; the shape of the end face working tooth profile curve is determined by a tooth tip control point P, an inter-tooth control point Pand a tooth bottom control point P; specifically, the combination types of the working tooth profile curves of the small wheel and the big wheel are CP from the tooth tip to the tooth root, where C and P represent a circular arc and a parabola, respectively, the circular arc is an upper curve of the working tooth profile, and the parabola is a lower curve of the working tooth profile; the tooth root transition curve is a Hermite curve determined by the tooth bottom control point Pand the tooth root control point P, and the tooth root transition curve is smoothly connected with the lower curve of the working tooth profile at the tooth bottom control point P.

Further, the tooth tip control point Pof the left working tooth profile of the small wheel and the big wheel is determined by a tooth tip circle radius Rand an offset angle χ, where χis the angle at which a tooth tip reference point Jof the small wheel and the big wheel rotates clockwise around the center of the circle; the tooth bottom control point Pis determined by a tooth bottom circle radius Rand an offset angle χ, where χis the angle at which a tooth bottom reference point Jof the small wheel and the big wheel rotates clockwise around the center of the circle; wherein the tooth tip reference point Jof the small wheel and the big wheel is an intersection point with the small wheel and the big wheel having an involute with the same base circle radius and an end face pressure angle and a tooth tip circle with the same radius R, respectively; and the tooth bottom reference point Jof the small wheel and the big wheel is an intersection point with the small wheel and the big wheel having an involute with the same base circle radius and an end face pressure angle and a tooth bottom circle with the same radius R, respectively.

Further, the tooth surface contact line between the small wheel and the big wheel is determined by the following method:

in equation (2), kis a linear proportional coefficient of the motion of the meshing point; iis a transmission ratio between the small wheel and the big wheel;

Further, the specific structures of the left end face tooth profiles of the small wheel and the big wheel are determined by the following method:

Hermite curve, which is the left tooth root transition curve of the gear tooth end face of the small wheel and the big wheel, is determined by points Pand Pand their tangent vectors Tand T, Pis determined by the tooth root circle radius Rand the angle δ, where δis an acute angle included between the radial vector of point Pand the coordinate axis x, so as to obtain the parameter equation of the left tooth root transition curve determined by the tooth root control point Pand the tooth bottom control point P, that is, the Hermite curve:

λis a central angle corresponding to the tooth thickness of the pitch circle of the small wheel.

Further, the small wheel is used to connect an input shaft, and the big wheel is used to connect an output shaft.

Further, the input shaft and output shaft connected with the small wheel and the big wheel are interchangeable.

Further, one of the small wheel and the big wheel is connected with the input shaft, the input shaft is connected with a driver, and the driver is capable of driving the small wheel or the big wheel to rotate forward and backward.

The technical scheme provided by the embodiment of the present disclosure has the following beneficial effects.

In order to make the purpose, technical scheme and advantages of the present disclosure more clear, the embodiments of the present disclosure will be further described with reference to the attached drawings hereinafter. A preferred embodiment of many possible embodiments of the present disclosure is described hereinafter, which is intended to provide a basic understanding of the present disclosure, but is not intended to identify key or decisive elements of the present disclosure or limit the scope to be protected.

In all examples shown and discussed herein, any specific values should be interpreted as illustrative only and not as a limitation. Therefore, other examples of exemplary embodiments may have different values.

Techniques, methods and devices known to those skilled in the art may not be discussed in detail, but in appropriate cases, the techniques, methods and devices should be regarded as part of the authorization specification.

It should be noted that similar numbers and letters indicate similar items in the following drawings. Therefore, once an item is defined in one drawing, the item does not need to be further discussed in subsequent drawings. At the same time, it should be understood that for the convenience of description, the dimensions of various parts shown in the drawings are not drawn to scale.

In the description of the present disclosure, it should be noted that the circuits, electronic components and modules involved in the present disclosure are all in the prior art, which can be completely implemented by those skilled in the art. Needless to say, the contents protected by the present disclosure do not involve the improvement of the internal structure and method.

Further, it should be noted that unless otherwise specified and limited, the terms “installation” and “connection” should be broadly understood, for example, the connection can be fixed connection, detachable connection or integrated connection; or mechanical connection or electrical connection; or direct connection, indirect connection through an intermediate medium, or communication inside two elements. For those skilled in the art, the specific meanings of the above terms in the present disclosure can be understood in specific situations.

Referring to, an embodiment of the present disclosure provides a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola, which is applied to the reduction transmission with a transmission ratio of 3 between parallel shafts. The coincidence degree therebetween is designed to be ε=2.4. Its structure is shown in, including a small wheeland a big wheel. The small wheeland the big wheelform a gear pair. The small wheelis connected with the input shaft. The input shaftis fixedly connected with a driving motorthrough a coupling. The big wheelis connected with the output shaft, that is, the big wheelis connected with the driven load through the output shaft. The axes of the small wheeland the big wheelare parallel to each other.is a schematic diagram of a spatial meshing coordinate system of a parabolic tooth trace gear mechanism with a combined tooth profile of an end face circular arc and a parabola according to the present disclosure.

Referring to, the pitch cylinderof the small wheel has a radius of R, the tooth top circle of the small wheel has a radius of Rand the tooth root circle has a radius of R. The outer surface of the tooth root cylinder of the small wheel is uniformly distributed with gear teeth with a parabolic tooth trace structure. Its structure is formed by the motion of the end face tooth profile curve of the small wheel along the tooth surface contact line with the contact point, and the contact line is an axisymmetric parabola after being unfolded along the pitch cylindrical surface of the small wheel. The end face tooth profile of the gear of the small wheel is axisymmetric, that is, the left tooth profile and the right tooth profile of the end face are axisymmetric. Taking the left end face tooth profile of the small wheel as an example, the left end face tooth profile consists of the upper circular arc curveof the left end face working tooth profile of the small wheel, the lower parabolaof the left end face working tooth profile, and the left tooth root transition curve of the end face (that is, the Hermite curve) from the tooth tip to the tooth root in sequence.

Referring to, the pitch cylinderof the big wheel has a radius of R, the tooth top circle of the big wheel has a radius of Rand the tooth root circle has a radius of R. The outer surface of the tooth root cylinder of the big wheel is uniformly distributed with gear teeth with a parabolic tooth trace structure. Its structure is formed by the motion of the end face tooth profile curve of the big wheel along the tooth surface contact line with the contact point, and the contact line is an axisymmetric parabola after being unfolded along the pitch cylindrical surface of the big wheel. The end face tooth profile of the gear of the big wheel is axisymmetric, that is, the left tooth profile and the right tooth profile of the end face are axisymmetric. Taking the left end face tooth profile of the big wheel as an example, the left end face tooth profile consists of the upper circular arc curveof the left end face working tooth profile of the big wheel, the lower parabolaof the left end face working tooth profile, and the left tooth root transition curve of the end face (that is, the Hermite curve) from the tooth tip to the tooth root in sequence.

The working tooth profile of the end faces of the small wheel and the big wheel is the combined tooth profile of the end face circular arc and the parabola, and is axisymmetric from left to right. The right tooth profile of the end face can be obtained by the axial symmetry of the left tooth profile of the end face. Left working tooth profile curves are formed by smoothly connecting two plane curves (a circular arc and a parabola) at an inter-tooth control point P, an inter-tooth control point Gof a right tooth profile coincides with a node Pwhen the small wheel and the big wheel are installed, and the control point Gis obtained by the axial symmetry of the inter-tooth control point Pof a left working tooth profile curve; the shape of the end face working tooth profile curve is determined by a tooth tip control point P, an inter-tooth control point Pand a tooth bottom control point P, specifically, the combination types of the working tooth profile curves of the small wheel and the big wheel are CP from the tooth tip to the tooth root, where “C and P” represent a circular arc (Cir) and a parabola (Par), respectively, the circular arc is an upper curve of the working tooth profile, and the parabola is a lower curve of the working tooth profile; the tooth root transition curve is a Hermite curve (Her) determined by the tooth bottom control point Pand the tooth root control point P, and the tooth root transition curve is smoothly connected with the lower curve of the working tooth profile at the tooth bottom control point P.

The tooth tip control point Pof the left working tooth profile of the small wheel and the big wheel is determined by a tooth tip circle radius Rand an offset angle χ, where χis the angle at which a tooth tip reference point Jof the small wheel and the big wheel rotates clockwise around the center of the circle; the tooth bottom control point Pis determined by a tooth bottom circle radius Rand an offset angle χ, where χis the angle at which a tooth bottom reference point Jof the small wheel and the big wheel rotates clockwise around the center of the circle; wherein the tooth tip reference point Jof the small wheel and the big wheel is an intersection point with the small wheel and the big wheel having an involute with the same base circle radius and an end face pressure angle and a tooth tip circle with the same radius R, respectively; and the tooth bottom reference point Jof the small wheel and the big wheel is an intersection point with the small wheel and the big wheel having an involute with the same base circle radius and an end face pressure angle and a tooth bottom circle with the same radius R, respectively.